Many games of strategy were played in the Middle Ages, check out the links below:

Fox and Geese
http://www.osv.org/kids_zone/foxgeese/

Warwick Trebuchet
http://www.warwicksiege.com/flash_game/flash_game.asp

Smash the Castle
http://www.gamesonline.fm/fighting-games/smash-the-castle

Destroy the Castle
http://www.pbs.org/wgbh/nova/lostempires/trebuchet/destroywave.html

Jousting
http://www.tudorbritain.org/joust/

Nine Mens Morris
http://alumnus.caltech.edu/~leif/games/Morris/index.html

Chess
http://www.kidchess.com/gamestoplay.html

Checkers
http://kids.aol.com/games/checkers/

Back to School in the Middle Ages
http://www.museumoflondon.org.uk/London-Wall/Whats-on/Galleries/medieval/Games/Game+1.htm

Shopping Spree in the Middle Ages
http://www.museumoflondon.org.uk/London-Wall/Whats-on/Galleries/medieval/Games/Game+3.htm